Seven Square Numbers

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
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Seven Square Numbers

Add the sum of the squares of four numbers between $10$ and $20$ to the sum of the squares of three numbers less than $6$ to make the square of another, larger, number.